The model of a flat (Euclidean) expansive homogeneous and isotropic relativistic Universe in the light of the Wilkinson Microwave Anisotropy Probe (WMAP) observations

The Wilkinson Microwave Anisotropy Probe (WMAP) confirmed the model of a flat (Euclidean) expansive homogeneous and isotropic relativistic universe with the total zero mass (energy), which describes the properties of our observed expansive homogeneous and isotropic relativistic Universe in the first (linear, Newtonian or classical-mechanical) approximation.     

Matter-space-time properties of the Universe

In the expansive nondecelerative homogeneous and isotropic relativistic Universe there take place: the permanent constant maximum possible creation of matter, the relativistic increase of mass of expanding objects, the relativistic dilatation of time of expanding objects, the relativistic contraction of radial length of expanding objects, and the relativistic dilatation of angular dimensions of expanding remote objects.Editor's Note: The delay in publishing this paper was due to an unfortunate oversight connected with the late Professor Kopal's death.     

Cosmological Evolution of String Effective Gravitation with a Dilaton Potential and Higher-Loop Corrections. I

Cosmological evolution is investigated within the framework of low-energy string gravitation with higher-loop corrections to the dilaton coupling functions in the presence of a dilaton potential and a nongravitational source. It is shown that for homogeneous and isotropic models with a flat space, the cosmological system of equations reduces to an autonomous, third-order, dynamical system. Subclasses of models with a constant dilaton, which provide the basis for various cosmological mechanisms of dilaton stabilization, are considered. A class of solutions is distinguished with asymptotic scaling behavior of the energy density of the dilaton field.     

Scalar perturbations in two-temperature cosmological plasmas

We study the properties of density perturbations of a two-component plasma with a temperature difference on a homogeneous and isotropic background. For this purpose, we extend the general relativistic gauge-invariant and covariant (GIC) perturbation theory to include a multifluid with a particular equation of state (ideal gas) and imperfect fluid terms due to the relative energy flux between the two species. We derive closed sets of GIC vector and subsequently scalar evolution equations. We then investigate solutions in different regimes of interest. In particular, we study long-wavelength and arbitrary-wavelength Langmuir and ion-acoustic perturbations. The harmonic oscillations are superposed on a Jeans-type instability. We find a generalized Jeans criterion for collapse in a two-temperature plasma, which states that the species with the largest sound velocity determines the Jeans wavelength. Furthermore, we find that within the limit for gravitational collapse, initial perturbations in either the total density or charge density lead to a growth in the initial temperature difference. These results are relevant for the basic understanding of the evolution of inhomogeneities in cosmological models.     

Cosmological Dynamics of Brane Models and Vacuum Effects

The imposition of boundary conditions on the background fields of brane-world models leads to nonzero vacuum averages for the corresponding energy-momentum tensor. Methods from the qualitative theory of dynamic systems are used in this paper to study the cosmological evolution generated by this tensor. All the possible types of cosmological dynamics are examined for models with homogeneous and isotropic subspaces on the branes and the behavior of the corresponding solutions is studied in the early and late stages of evolution.     

Exact solutions to Kaluza-Klein cosmologies

We consider general methods to find exact solutions of Kaluza-Klein cosmologies with phenomenological matter and show some general conclusions about factorwise homogeneous and isotropic models.     

The model of a flat (Euclidean) expansive homogeneous and isotropic relativistic universe in the light of the general relativity,quantum mechanics,and observations

Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too.     

Why Newtonian gravity is reliable in large-scale cosmological simulations

Until now, it has been common to use Newtonian gravity to study the non-linear clustering properties of large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the analysis (e.g. near the horizon scale). In this work we will provide confirmation of the use of Newtonian gravity in cosmology, based on the relativistic analysis of weakly non-linear situations to third order in perturbations. We will show that, except for the gravitational-wave contribution, the relativistic zero-pressure fluid equations perturbed to second order in a flat Friedmann background coincide exactly with the Newtonian results. We will also present the pure relativistic correction terms appearing in the third order. The third-order correction terms show that these terms are the linear-order curvature perturbation times the second-order relativistic/Newtonian terms. Thus, the pure general relativistic corrections in the third order are independent of the horizon scale and are small when considering the large-scale structure of the Universe because of the low-level temperature anisotropy of the cosmic microwave background radiation. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to second order, and that the third-order correction terms are small, our result has the important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably as the simulation scale approaches and even goes beyond the horizon. In a complementary situation, where the system is weakly relativistic (i.e. far inside the horizon) but fully non-linear, we can employ the post-Newtonian approximation. We also show that in large-scale structures, the post-Newtonian effects are quite small.     

The Copernican principle in compact space–times

Copernicus realized that we are not at the centre of the Universe. A universe made finite by topological identifications introduces a new Copernican consideration: while we may not be at the geometric centre of the Universe, some galaxy could be. A finite universe also picks out a preferred frame: the frame in which the universe is smallest. Although we are not likely to be at the centre of the Universe, we must live in the preferred frame (if we are at rest with respect to the cosmological expansion). We show that the preferred topological frame must also be the comoving frame in a homogeneous and isotropic cosmological space–time. Some implications of topologically identifying time are also discussed.     

A Class of higher dimensional spherically symmetric cosmological model in Lyra geometry

Exact analytical solutions are obtained for a higher dimensional spherically symmetric inhomogeneous metric in presence of a mass-less scalar field with a flat potential within the framework of Lyra geometry. Assuming a homogeneous scalar field, we have shown that the metric can be reduced to a generalized FRW type.     

Isotropic Homogeneous Universe with a Bulk Viscous Fluid in Lyra Geometry

Exact solutions are obtained for an isotropic homogeneous universe with a bulk viscous fluid in the cosmological theory based on Lyra’s geometry. The viscosity coefficient of the bulk viscous fluid is assumed to be a power function of the mass density. Cosmological models with time dependent displacement field have been discussed for a constant value of the deceleration parameter. Finally some possibilities of further problems and their investigations have been pointed out.     

Observational manifestations of prerecombination protoobjects

We consider the image formation for an extremely distant source in an optically dense, homogeneous, and isotropic medium. We show that the angular size of the image would presently be θ₀ ≈ 10′, irrespective of the initial redshift z. Parameters of the inhomogeneities capable of producing the observed effect were estimated. We note that this effect should be taken into account for the baryon density fluctuations that were damped according to Silk at the prerecombination epoch. The spot radiation spectrum is shown to be a diluted Planckian spectrum with a dilution factor much larger than unity. We also point out the presence of peculiar tangential polarization in the spot, which reaches several tens of percent at the spot edge. All these observational features clearly distinguish the fluctuations under consideration from the standard fluctuations.     

Ages of the universe for FRW-type models in wesson's 5D variable mass theory of gravity

The age of the universe is computed for spatially homogeneous and isotropic cosmological models of the relativistic Wesson's 5D variable mass theory of gravity. It is shown that if the pressure in the mass dimension is negligible, ages old enough to agree with the observations can only be obtained if the cosmological constant is different from zero. In addition, unlike the standard FRW models in Einstein's 4D theory, the age value itself is not affected by the nature of the matter content (matter and radiation dominated models give the same age).     

Theory of linear cosmological perturbations in flat space-time theory of gravitation

Covariant linear cosmological perturbations are considered in flat space-time theory of gravitation. The background metric is not altered. The perturbed energy-momentum is given. The basic equations for the propagation of the perturbations are presented. The perturbed equations for a homogeneous, isotropic universe are stated.     

Cosmological parameters and cosmic topology

Geometry constrains but does not dictate the topology of the three-dimensional space. In a locally spatially homogeneous and isotropic universe, however, the topology of its spatial section dictates its geometry. We show that, besides determining the geometry, the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of setting constraints on the density parameters associated with dark matter (Ω_m) and dark energy  (Ω_Λ)  . By assuming the Poincaré dodecahedral space as the circles-in-the-sky detectable topology of the spatial sections of the Universe, we re-analyse the constraints on the density parametric plane  Ω_m–Ω_Λ  from the current Type Ia supernova plus X-ray gas mass fraction data, and show that a circles-in-the sky detection of the dodecahedral space topology gives rise to strong and complementary constraints on the region of the density parameter plane currently allowed by these observational data sets.     

Anisotropic ghost dark energy cosmological model with hybrid expansion law

In this paper, we study the anisotropic Bianchi type-VI₀ metric filled with dark matter and anisotropic ghost dark energy. We have solved the Einstein's field equations by considering hybrid expansion law (HEL) for the average scale factor. It is found that at later times the universe becomes spatially homogeneous, isotropic and flat. From a state finder diagnosis, it is found that our model is having similar behavior like ɅCDM model at late phase of cosmic time.     

Stability of the inflation in R2 cosmology with massless conformal quantum fields

A semiclassical higher-derivative theory of gravity is investigated for conformally invariant free quantum fields in homogeneous and isotropic spacetime with no cosmological constant nor classical source. In the spatially flat case the stability of the de Sitter solution is studied. Moreover, the Minkowski solution is found to be unstable.Fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas.     

Relativistic corrections to the multiple scattering effect on the Sunyaev–Zel'dovich effect in the isotropic approximation

We extend the formalism for the calculation of the relativistic corrections to the Sunyaev–Zel'dovich effect for clusters of galaxies and include the multiple scattering effects in the isotropic approximation. We present the results of the calculations by the Fokker–Planck expansion method as well as by the direct numerical integration of the collision term of the Boltzmann equation. The multiple scattering contribution is found to be very small compared with the single scattering contribution. For high-temperature galaxy clusters of     the ratio of both the contributions is −0.2 per cent in the Wien region. In the Rayleigh–Jeans region the ratio is −0.03 per cent. Therefore the multiple scattering contribution is safely neglected for the observed galaxy clusters.     

Irreversible Matter Creation in Inflationary Cosmology

Irreversible matter creation is investigated in a two-component (scalar field and ordinary matter) cosmological fluid in a homogeneous spatially flat and isotropic Friedmann-Robertson-Walker (FRW) inflationary Universe during its reheating era. The thermodynamics of open systems as applied together with the gravitational field equations to the two-component cosmological fluid leads to a generalisation of the elementary reheating theory in which the decay (creation) pressures are explicitly considered as parts of the fluid stress-energy tensor. Particular models describing coherently oscillating scalar waves and leading to a high particle production at the beginning of the oscillatory period are considered too. This revised version was published online in July 2006 with corrections to the Cover Date.